Three-phase power worksheet with answers

Free printable Three-phase power worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
ABCVL​ = 690 VIL​ = ?NZ = 24 + j18 Ωper phase

A balanced Y-connected load has an impedance of 24 + j18 Ω per phase. It is supplied from a balanced three-phase source with a line-to-line voltage of 690 V. Find the magnitude of the line current IL.

VL = 690 VZ = 24 + j18 Ω per phase
IL = A
2.Easy
ABCVL​ = 415 VIL​ = ?Z = 12 + j16 Ωper phase

A balanced Δ-connected load has an impedance of 12 + j16 Ω per phase. It is supplied from a balanced three-phase source with a line-to-line voltage of 415 V. Find the magnitude of the line current IL.

VL = 415 VZ = 12 + j16 Ω per phase
IL = A
3.Medium
ABCVL​ = 400 VNZ = 15 + j20 Ωper phase

A balanced Y-connected load with an impedance of 15 + j20 Ω per phase is connected to a balanced three-phase supply with a line-to-line voltage of 400 V. Find the total real power P absorbed by the load in kW.

VL = 400 VZ = 15 + j20 Ω per phase
P = kW
4.Medium
ABCVL​ = 208 VIL​ = 20 Acos φ = 0.8lagging

A balanced three-phase load draws a line current of 20 A from a supply with a line-to-line voltage of 208 V. The power factor is 0.8 lagging. Find the total real power P drawn by the load in kW.

VL = 208 VIL = 20 Acos φ = 0.8
P = kW
5.Hard
P = 150 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 150 kW at a power factor of 0.65 lagging from a 400 V (line-to-line), 50 Hz supply. A three-phase capacitor bank in parallel with the load must raise the overall power factor to 0.95 lagging. The real power stays the same. The capacitors are connected in Δ. Find the capacitance Cph of each capacitor in µF.

P = 150 kWpf1 = 0.65pf2 = 0.95VL = 400 Vf = 50 Hz
Cph = µF
6.Hard
P = 120 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 120 kW at a power factor of 0.72 lagging from a 480 V (line-to-line), 50 Hz supply. A three-phase capacitor bank in parallel with the load must raise the overall power factor to 0.9 lagging. The real power stays the same. The capacitors are connected in Δ. Find the capacitance Cph of each capacitor in µF.

P = 120 kWpf1 = 0.72pf2 = 0.9VL = 480 Vf = 50 Hz
Cph = µF

Answer key

  1. 1. IL = 13.28 A
  2. 2. IL = 35.94 A
  3. 3. P = 3.84 kW
  4. 4. P = 5.764 kW
  5. 5. Cph = 836 µF
  6. 6. Cph = 265 µF

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